September 27, 2006

The Cartisan Plane?! (and other things!)


Hi guys! It's Cherrie again, here to make another attempt to earn a badge, and to help my fellow students. Again, thanks to everyone who congratulated me, and thought my last scribe was great. Much appreciated :).
Today in class, Mr. K started us off with the following problems:
Find the related angle
a) 220°
b) 150°
c) 400°

Which, as a class, resulted in the answers:
a) 40°
b) 80°
and c) 40°
How did we get to these answers, you ask? You're probably wondering what the related angle of an angle is. The related angle is the smallest angle made with the x-axis. As an example, I'll show you how we got to the answer for letter a.

On the x-axis we have the landmark of 180°. If you start from the right, where it's marked 180°, and if we were able to measure accurately, 220° would approximately appear where I've marked it, so basically, the orange shaded region is 220°.

The peach shaded region, is what we call the related angle, because just like the explaination said, it's the smallest angle made with the x-axis.

Now how we got the 40° as the related angle of 220°?
Because the angle lies between the x-axis, which is the 180° landmark, and ends at the 220° mark, all we did was find the difference between those two degrees. We all know how to do that now, don't we? Simply subtract 180° from 220°, and therefore, we get 40°. Calculating the related angles of letters b and c are done the same way. To me, it's easier to understand when I draw a diagram of it.
(sorry my coloring looks weird!)

Mr. K also discussed with the class about the Cartisan plane. He mentioned that sin values lie on the y-axis and the cos values lie on the x-axis.
Concerning angles and related angles, he told us that as an angle gets bigger on the plane, the sin value becomes greater -- it eventually reaches a maximum of 1, and 90°. As it passes 90°, it'll begin to back down to 180°.
Remember that if the angle goes past 180°, and is underneath the x-axis, the angle becomes negative, and will have a minimum value.

A diagram can explain what's mentioned above.

On another note, on the Cartisan Plane, if your cos Θ is negative, your angle will lay on the x-axis, in either quads 2 or 3. However if your cos Θ is positive, it will lay in either quads 1 or 4.
If your sin Θ is positive, your angle will lay on the y-axis, in either quads 1 or 2. Otherwise, if your sin Θ is negative, it will lay in quads 3 or 4.
"Mathematics is the science of patterns"
That's what Mr. K has taught us. We also were asked to solve for x in the following equations:
a) 2x + 1 = 0
2x = -1
x = -1/2
b) 2x² - x - 1 = 0
(2x + 1)(x - 1)
x = -1/2
x = 1
c) 3x - 4 = 7x + 2
-6 = 4x
x = -3/2
Mr. K decided to re-write these equations and replace the x's for sin Θ and cos Θ.
We re-wrote them, and we did get the same answers for all of them. This means that renaming the variable into sin Θ and cos Θ doesn't make a difference, but Mr. K said we'd have to take one extra step into solving the equation -- we'd have to figure out what Θ equals.
I gave it a shot, and I hope you guys understood my scribe. I'm sorry for the late post, I had volleyball practice til 8:45 pm, and I'm pooped :.
And the moment you've all been waiting for.
The next scribe will be m@rk!


  1. Hi Cherrie,

    Your diagrams do make it easier to understand; we must both be visual learners?! --at least to some extent. Your scribe explanations and your including the quote from Mr. K,
    "Mathematics is the science of patterns."
    has helped me in my learning! Thank you!


  2. Cherrie!

    your diagrams are awesome!. =D